Local existence and uniqueness for a fractional SIRS model with Mittag-Leffler law

TL;DR

This paper investigates a fractional SIRS epidemic model with Atangana-Baleanu-Caputo derivatives, establishing existence, uniqueness, and stability of solutions, and providing numerical methods for solving the model.

Contribution

It introduces a novel fractional SIRS model with ABC derivatives, proving solution existence, uniqueness, stability, and implementing numerical solutions.

Findings

Existence and uniqueness of solutions proved.

Stability analysis of the model conducted.

Numerical solutions obtained using Adams-Bashforth-Moulton method.

Abstract

In this paper, we study an epidemic model with Atangana-Baleanu-Caputo (ABC) fractional derivatives. We obtain a special solution using an iterative scheme via Laplace transformation. Uniqueness and existence of solution using the Banach fixed point theorem are studied. A detailed analysis of the stability of the special solution is presented. Finally, our generalized model in the ABC derivative sense is solved numerically by the Adams-Bashforth-Moulton method.